Transcript Solving Systems of Equations

Warm-up
Twice the supplement of an angle is ten
times the measure of the angle itself. Find
the measure of both angles.
Three times the complement of an angle is
seven times the measure of the angle itself.
Find the measure of both angles.
Solving Systems of
Linear Equations
What is a System of
Linear Equations?
Wikipedia says it’s…
A collection of linear equations that use the
same variables
What does it mean to be a
solution?
It’s a coordinate pair that “works” in both
equations
Graphically: It’s where the lines intersect
3 Different Methods
• Graphing
• Substitution
• Elimination/Linear
Combination
Look at the Graph and Find the
Solution to the system of equations
There are actually 3 cases
Case 1
Case 2
Case 3
One Solution
NO Solutions
Infinite Solutions
Ok so now let’s look at it
algebraically
This is where the other
two methods come in.
Substitution
Elimination/Linear Combination
Substitution
Works best when one of your coefficients is 1
(ex: x + 3y = 7, x has a coefficient of 1 and
y has one of 3.)
First, get the variable with the coefficient of
1 alone (x = -3y + 7).
Next, substitute the expression in for the
variable you isolated into the 2nd equation.
Now you have an equation with one variable,
so solve for that variable. Then, plug your
answer into an original equation to find
the other variable.
Example
2 x  3 y  2

 4 x  y  24
Elimination/Linear
Combination
First make one of the variables have
opposite coefficients (if not already done)
by multiplying.
Then you will add the equations together
which will cancel out one of the variables
and allow you to solve for the other.
Then you will plug it back into your equation
and find the other variable.
Example
 2x  y  9

3
x

y

16

Try another…
2 x  y  9

3x  4 y  14
How about some more!!
12 x  13 y  2

6 x  6.5 y  2
12 x  3 y  6

4 x  y  2
Flipped
Review
3 Different Methods
• Graphing
• Substitution
• Elimination/Linear
Combination
Look at the Graph and Find the
Solution to the system of equations
There are actually 3 cases
Case 1
Case 2
Case 3
One Solution
NO Solutions
Infinite Solutions
Substitution
Works best when one of your coefficients is 1
(ex: x + 3y = 7, x has a coefficient of 1 and
y has one of 3.)
First, get the variable with the coefficient of
1 alone (x = -3y + 7).
Next, substitute the expression in for the
variable you isolated into the 2nd equation.
Now you have an equation with one variable,
so solve for that variable. Then, plug your
answer into an original equation to find
the other variable.
Example
2 x  3 y  2

 4 x  y  24
Elimination/Linear
Combination
First make one of the variables have
opposite coefficients (if not already done)
by multiplying.
Then you will add the equations together
which will cancel out one of the variables
and allow you to solve for the other.
Then you will plug it back into your equation
and find the other variable.
Example
 2x  y  9

3
x

y

16
